Imidazolium galactarate

In the structure of title compound, 2(C3H5N2^+^) C~6~H~8~O~8~^2-^ . 2H~2~O the galactarate dianions have crystallographic inversion symmetry and together with the water molecules of solvation form hydrogen-bonded sheet substructures which extend along the (110) planes in the unit cell. The imidazolium cations link these sheets peripherally down c through carboxyl O...H-N,N'---H...O(hydroxyl) bridges, giving a three-dimensional framework structure.

catena-Poly[[[diaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3O1,O2:O1'-[tetraaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3-O1:O1',O2] dihydrate]

In the structure of polymeric title compound, {[Co2(C7H2N2O7)2(H2O)6] . 2H2O}n from the reaction of 3,5-dinitrosalicylic acid with cobalt(II) acetate, both slightly distorted octahedral Co(II) centres have crystallographic inversion symmetry. The coordination sphere about one Co centre comprises four O donors from two bidentate chelate O(phenolate), O(carboxyl) and bridging dianionic ligands and two water molecules [Co-O range, 2.0249(11)-2.1386(14)A] while that about the second Co centre has four water molecules and two bridging carboxyl O donor atoms [Co-O range, 2.0690(14)-2.1364(11)A]. The coordinated water molecules as well as the water molecules of solvation give water-water and water-carboxyl hydrogen-bonding interactions in the three-dimensional framework structure.

Poly[[diaquabis[mu-2-(4-fluorophenoxy)acetato-k2O1:O1']magnesium] 0.4-hydrate]

In the structure of the title compound, [Mg(H2O)2(C8H6FO3)2]n(0.4H2O)n, slightly distorted octahedral MgO6 complex units have crystallographic inversion symmetry, the coordination polyhedron comprising two trans-related water molecules and four carboxyl O-atom donors, two of which are bridging. Within the two-dimensional complex polymer which is parallel to (100), the coordinating water molecules form intermolecular O---H...O hydrogen-bonds with carboxylate and phenoxy O-atom acceptors, as well as with the partial-occupancy solvent water molecules.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].

Three-dimensional hydrogen-bonded structures in the guanidinium salts of the monocyclic dicarboxylic acids rac-trans-cyclohexane-1,2-dicarboxylic acid (2:1, anhydrous), isophthalic acid (1:1, monohydrate) and terephthalic acid (2:1, trihydrate).

The structures of bis(guanidinium)rac-trans-cyclohexane-1,2-dicarboxylate, 2(CH6N3+) C8H10O4- (I), guanidinium 3-carboxybenzoate monohydrate CH6N3+ C8H5O4- . H2O (II) and bis(guanidinium) benzene-1,4-dicarboxylate trihydrate, 2(CH6N3+) C8H4O4^2- . 3H2O (III) have been determined and the hydrogen bonding in each examined. All three compounds form three-dimensional hydrogen-bonded framework structures. In anhydrous (I), both guanidinium cations give classic cyclic R2/2(8) N--H...O,O'(carboxyl) and asymmetric cyclic R1/2(6) hydrogen-bonding interactions while one cation gives an unusual enlarged cyclic interaction with O acceptors of separate ortho-related carboxyl groups [graph set R2/2(11)]. Cations and anions also associate across inversion centres giving cyclic R2/4(8) motifs. In the 1:1 guanidinium salt (II), the cation gives two separate cyclic R1/2(6) interactions, one with a carboxyl O-acceptor, the other with the water molecule of solvation. The structure is unusual in that both carboxyl groups give short inter-anion O...H...O contacts, one across a crystallographic inversion centre [2.483(2)\%A], the other about a two-fold axis of rotation [2.462(2)\%A] with a half-occupancy hydrogen delocalized on the symmetry element in each. The water molecule links the cation--anion ribbon structures into a three-dimensional framework. In (III), the repeating molecular unit comprises a benzene-1,4-dicarboxylate dianion which lies across a crystallographic inversion centre, two guanidinium cations and two water molecules of solvation (each set related by two-fold rotational symmetry), and a single water molecule which lies on a two-fold axis. Each guanidinium cation gives three types of cyclic interactions with the dianions: one R^1^~2~(6), the others R2/3(8) and R3/3(10) (both of these involving the water molecules), giving a three-dimensional structure through bridges down the b cell direction. The water molecule at the general site also forms an unusual cyclic R2/2(4) homodimeric association across an inversion centre [O--H...O, 2.875(2)\%A]. The work described here provides further examples of the common cyclic guanidinium cation...carboxylate anion hydrogen-bonding associations as well as featuring other less common cyclic motifs.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Interocular symmetry in myopic anisometropia

Purpose: To investigate the interocular symmetry of optical, biometric and biomechanical characteristics between the fellow eyes of myopic anisometropes. Methods: Thirty-four young, healthy myopic anisometropic adults (≥ 1 D spherical equivalent difference between eyes) without amblyopia or strabismus were recruited. A range of biometric and optical parameters were measured in both eyes of each subject including; axial length, ocular aberrations, intraocular pressure (IOP), corneal topography and biomechanics. Ocular sighting dominance was also measured. Results: Mean absolute spherical equivalent anisometropia was 1.70 ± 0.74 D and there was a strong correlation between the degree of anisometropia and the interocular difference in axial length (r = 0.81, p < 0.001). The more and less myopic eyes displayed a high degree of interocular symmetry for the majority of biometric, biomechanical and optical parameters measured. When the level of anisometropia exceeded 1.75 D, the more myopic eye was more likely to be the dominant sighting eye than for lower levels of anisometropia (p=0.002). Subjects with greater levels of anisometropia (> 1.75 D) also showed high levels of correlation between the dominant and non-dominant eyes in their biometric, biomechanical and optical characteristics. Conclusions: Although significantly different in axial length, anisometropic eyes display a high degree of interocular symmetry for a range of anterior eye biometrics and optical parameters. For higher levels of anisometropia, the more myopic eye tends to be the dominant sighting eye.

Symmetry of in-shoe force signatures in athletes under field conditions : an application for injury prevention

The aetiology behind overuse injuries such as stress fractures is complex and multi-factorial. In sporting events where the loading is likely to be uneven (e.g. hurdling and jumps), research has suggested that the frequency of stress fractures seems to favour the athlete’s dominant limb. The tendency for an individual to have a preferred limb for voluntary motor acts makes limb selection a possible factor behind the development of unilateral overuse injuries, particularly when repeatedly used during high loading activities. The event of sprint hurdling is well suited for the study of loading asymmetry as the hurdling technique is repetitive and the limb movement asymmetrical. Of relevance to this study is the high incidence of Navicular Stress Fractures (NSF) in hurdlers, with suggestions there is a tendency for the fracture to develop in the trail leg foot, although this is not fully accepted. The Ground Reaction Force (GRF) with each foot contact is influenced by the hurdle action, with research finding step-to-step loading variations. However, it is unknown if this loading asymmetry extends to individual forefoot joints, thereby influencing stress fracture development. The first part of the study involved a series of investigations using a commercially available matrix style in-shoe sensor system (FscanTM, Tekscan Inc.). The suitability of insole sensor systems and custom made discrete sensors for use in hurdling-related training activities was assessed. The methodology used to analyse foot loading with each technology was investigated. The insole and discrete sensors systems tested proved to be unsuitable for use during full pace hurdling. Instead, a running barrier task designed to replicate the four repetitive foot contacts present during hurdling was assessed. This involved the clearance of a series of 6 barriers (low training hurdles), place in a straight line, using 4 strides between each. The second part of the study involved the analysis of "inter-limb" and "within foot loading asymmetries" using stance duration as well as vertical GRF under the Hallux (T1), the first metatarsal head (M1) and the central forefoot peak pressure site (M2), during walking, running, and running with barrier clearances. The contribution to loading asymmetry that each of the four repetitive foot contacts made during a series of barrier clearances was also assessed. Inter-limb asymmetry, in forefoot loading, occurred at discrete forefoot sites in a non-uniform manner across the three gait conditions. When the individual barrier foot contacts were compared, the stance duration was asymmetrical and the proportion of total forefoot load at M2 was asymmetrical. There were no significant differences between the proportion of forefoot load at M1, compared to M2; for any of the steps involved in the barrier clearance. A case study testing experimental (discrete) sensors during full pace sprinting and hurdling found that during both gait conditions, the trail limb experienced the greater vertical GRF at M1 and M2. During full pace hurdling, increased stance duration and vertical loading was a characteristic of the trail limb hurdle foot contacts. Commercially available in-shoe systems are not suitable for on field assessment of full pace hurdling. For the use of discrete sensor technology to become commonplace in the field, more robust sensors need to be developed.

Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Generalized IBE in the exponent-inversion framework

The purpose of this chapter is to provide an abstraction for the class of Exponent-Inversion IBE exemplified by the [Bscr ][Bscr ]2 and [Sscr ][Kscr ] schemes, and, on the basis of that abstraction, to show that those schemes do support interesting and useful extensions such as HIBE and ABE. Our results narrow, if not entirely close, the “flexibility gap” between the Exponent-Inversion and Commutative-Blinding IBE concepts.

Breaking time-inversion invariance through decoherence : energetic consequences for attosecond neutron scattering

Nuclei and electrons in condensed matter and/or molecules are usually entangled, due to the prevailing (mainly electromagnetic) interactions. However, the "environment" of a microscopic scattering system (e.g. a proton) causes ultrafast decoherence, thus making atomic and/or nuclear entanglement e®ects not directly accessible to experiments. However, our neutron Compton scattering experiments from protons (H-atoms) in condensed systems and molecules have a characteristic collisional time about 100|1000 attoseconds. The quantum dynamics of an atom in this ultrashort, but ¯nite, time window is governed by non-unitary time evolution due to the aforementioned decoherence. Unexpectedly, recent theoretical investigations have shown that decoherence can also have the following energetic consequences. Disentangling two subsystems A and B of a quantum system AB is tantamount to erasure of quantum phase relations between A and B. This erasure is widely believed to be an innocuous process, which e.g. does not a®ect the energies of A and B. However, two independent groups proved recently that disentangling two systems, within a su±ciently short time interval, causes increase of their energies. This is also derivable by the simplest Lindblad-type master equation of one particle being subject to pure decoherence. Our neutron-proton scattering experiments with H2 molecules provide for the first time experimental evidence of this e®ect. Our results reveal that the neutron-proton collision, leading to the cleavage of the H-H bond in the attosecond timescale, is accompanied by larger energy transfer (by about 2|3%) than conventional theory predicts. Preliminary results from current investigations show qualitatively the same e®ect in the neutron-deuteron Compton scattering from D2 molecules. We interpret the experimental findings by treating the neutron-proton (or neutron-deuteron) collisional system as an entangled open quantum system being subject to fast decoherence caused by its "environment" (i.e., two electrons plus second nucleus of H2 or D2). The presented results seem to be of generic nature, and may have considerable consequences for various processes in condensed matter and molecules, e.g. in elementary chemical reactions.